Minh T. Tran

Bio: Minh T. Tran is an academic researcher from Texas Instruments. The author has contributed to research in topics: Discrete time and continuous time & Algebraic Riccati equation. The author has an hindex of 5, co-authored 16 publications receiving 80 citations. Previous affiliations of Minh T. Tran include Wichita State University.

Reduced order discrete-time models

Abstract: Linear shift-invariant discrete-time systems satisfying the two time scale property-are considered. Conditions for a complete separation of slow and fast subsystems are given. Subsystem regulator problems are investigated and the controllability property of the system is established based on the subsystem controllability properties. A subsystem controller design method is proposed depending on the separability of the slow and fast controls.

A note on the discrete Lyapunov and Riccati matrix equations

Abstract: Inequalities which are satisfied by the determinants of the positive definite solutions of the discrete algebraic Riccati and Lyapunov matrix equations are presented. The results give lower bounds for the product of the eigenvalues of the matrix solutions. Also for a discrete Lyapunov equation, an algorithm is presented to determine under what conditions a positive diagonal solution will exist. If all the conditions are satisfied, the algorithm also provides such a diagonal solution.

Decentralized control for two time-scale discrete-time systems

Abstract: Output feedback design of discrete-time decentralized systems with slow and fast modes is considered. Conditions for the complete separation of slow and fast subsystems are given. The slow and fast subsystem outputs, which are obtained by applying the slow and fast subcontrollers to the corresponding subsystems, will be shown to approximate those of the original system. Also, the composite control, when being applied to the original system, will place the eigenvalues sufficiently close to the desired locations.

On the well-posedness of discrete-time systems with slow and fast modes

Abstract: Linear shift-invariant discrete-time systems satisfying the two time-scale property are considered. Conditions for a complete separation of slow and fast subsystems are given. The composite controller will be formed from the slow and fast subsystem controllers. The slow and fast subsystem trajectories will be obtained and they will be shown to approximate those of the original system. Conditions for existence of the solutions of the subsystem regulator problems will also be given

Nash strategies for discrete-time systems with slow and fast modes

Abstract: Linear shift invariant discrete-time Nash games are considered. In particular, linear-quadratic infinite-time zero-sum Nash games for discrete-time systems with slow and fast modes are investigated. Derivation of near-optimal strategies which do not require any knowledge of the small singular perturbation parameter is presented based on the asymptotic behaviour of the solution.

Singular perturbations and time scales in control theory and applications: An overview

Abstract: This paper presents an overview of singular perturbations and time scales (SPaTS) in control theory and applications during the period 1984-2001 (the last such overviews were provided by [231, 371]). Due to the limitations on space, this is in way intended to be an exhaustive survey on the topic.

Singular perturbations in control problems

Abstract: Results on singularly perturbed control obtained since 1982 are reviewed. PACS number: 02.30.Yy DOI: 10.1134/S0005117906010012

Bounds in algebraic Riccati and Lyapunov equations: a survey and some new results

Abstract: This paper summarizes and investigates the relations of a number of bounds for the solutions of the algebraic Riccati and Lyapunov equations that have been reported during the last two decades. Also presented are bounds for the unified Riccati equation using the delta operator and it is shown that some bounds for the continuous and discrete Riccati equations can be unified by them.

On bounds of the Riccati and Lyapunov matrix equations

Abstract: Various bounds for the traces of the solutions of the algebraic Riccati and Lyapunov matrix equations are established in the continuous and discrete domain, respectively. The presented results give lower bounds for the sum of the eigenvalue of the matrix solutions.

Bounds for the eigenvalues of the solution of the discrete Riccati and Lyapunov equations and the continuous Lyapunov equation

Abstract: We present some bounds for the eigenvalues and certain sums and products of the eigenvalues of the solution of the discrete Riccati and Lyapunov matrix equations and the continuous Lyapunov matrix equation. Nearly all of our bounds for the discrete Riccati equation are new. The bounds for the discrete and continuous Lyapunov equations give a completion of some known bounds for the extremal eigenvalues and the determinant and the trace of the solution of the respective equation.